Question

Dennis plans to use 1150 ft of fence to enclose a rectangular pasture shown below. one side borders a river where there is already a thick hedge. it needs no fencing.

Answer 1

The pasture is in the shape of a rectangle only the widths are marked.

a. Let x be the width of the pasture as labeled. Write an expression for the length in terms of x.

b. Write an expression for the area of the pasture in terms of x.

(a) the hedge along the length . we need to consider the three sides for fencing.

To find the length we use the given information

Dennis plans to use 1150 ft of fence to enclose a rectangular pasture.

Perimeter of rectangle = 2L + 2W

the hedge along the length, so we perimeter becomes L + 2W

Perimeter = L +2W, Width is x and perimeter is 1150

1150 = L + 2x ( subtract 2x on both sides)

So length L = 1150 - 2x

(b)Area of rectangle = length * width

We got L = 1150 -2x and we know width is x

Area = (1150-2x)*x

`Area = 1150x - 2x^2` square feet